NCERT Solutions for Class 6 Maths Chapter 7 Fractions

Q.1 Write the fraction representing the shaded portion.

Answer :

(i) Number of parts = 4
Shaded portion = 2
\(\therefore \) Fraction = \(\frac{2}{4} \)
(ii) Number of parts = 9
Shaded portion = 8
\(\therefore \) Fraction = \(\frac{8}{9} \)
(iii) Number of parts = 8
Shaded portion = 4
\(\therefore \) Fraction = \(\frac{4}{8} \)
(iv) Number of parts = 4
Shaded portion = 1
\(\therefore \) Fraction = \(\frac{1}{4} \)
(v) Number of parts = 7
Shaded portion = 3
\(\therefore \) Fraction = \(\frac{3}{7} \)
(vi) Number of parts = 12
Shaded portion = 3
\(\therefore \) Fraction = \(\frac{3}{12} \)
(vii) Number of parts = 10
Shaded portion = 10
\(\therefore \) Fraction = \(\frac{10}{10} \)
(viii) Number of parts = 9
Shaded portion = 4
\(\therefore \) Fraction = \(\frac{4}{9} \)
(ix) Number of parts = 8
Shaded portion = 4
\(\therefore \) Fraction = \(\frac{4}{8} \)
(x) Number of parts = 2
Shaded portion = 1
\(\therefore \) Fraction = \(\frac{1}{2} \)

Q.2 Colour the part according to the given fraction.

Answer :

Q.3 Identify the error, if any.

Answer :

(i) The parts are not equal
Hence, this is not \(\frac{1}{2} \)
(ii) the parts are not equal
Hence, Shaded portion is not \(\frac{1}{4} \)
(iii) the parts are not equal
Hence, Shaded portion is not \(\frac{3}{4} \)

Q.4 What fraction of a day is 8 hours?

Answer :

Since, a day has 24 hours and we have 8 hours
\(\therefore \) Required fraction = \(\frac{8}{24} \)

Q.5 What fraction of an hour is 40 minutes?

Answer :

Since 1 hours = 60 minutes
\(\therefore \) Fraction of 40 minutes = \(\frac{40}{60} \)

Q.6 Arya, Abhimanyu, and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetable and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich.
(a) How can Arya divide his sandwiches so that each person has an equal share?
(b) What part of a sandwich will each boy receive?

Answer :

(a) Arya has divided the sandwich into 3 equal parts. So each person will get one part.
(b) Each boy receive \(\frac{1}{3} \)

Q.7 Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished?

Answer :

Total number of dresses to be dyed = 30
Number of dresses finished = 20
\(\therefore \) Required fraction = \(\frac {20}{30} = \frac{2}{3} \)

Q.8 Write the natural numbers from 2 to 12. What fraction of them are prime numbers?

Answer :

Natural numbers between 2 and 12 are;
2,3,4, 5, 6, 7, 8, 9, 10,11, 12
No. of given natural numbers = 11
No. of prime numbers = 5
Hence, fraction = \(\frac{5}{11} \)

Q.9 Write the natural numbers from 102 to 113. What fraction of them are prime numbers?

Answer :

Natural numbers from 102 to 113 are;
102,103,104,105,106, 107,108, 109,110, 111, 112,113
Total number of given natural numbers = 12
Prime numbers are 103, 107, 109, 113 Number of prime numbers = 4
Hence, fraction = \(\frac{4}{12} \) = \(\frac{1}{3} \)

Q.10 What fraction of these circles have X’s in them?

Answer :

Total number’of circles = 8
Number of circles having X’s in them = 4
Required fraction = \(\frac{4}{8} = \frac{1}{2} \)

Q.11 Kristin received a CD player for her birthday. She bought 3 CDs and received 5 others as gifts. What fraction of her total CDs did she buy and what fraction did she receive as gifts?

Answer :

Number of CDs bought by her from the market = 3
Number of CDs received as gifts = 5
Therefore Total number of CDs = 3 + 5 = 8
Therefore Fraction of CDs (bought) = \(\frac{3}{8} \)
and the fraction of CDs (gifted) = \(\frac{5}{8} \)

Q.1 Draw number lines and locate the points on them:
(a)\(\frac{1}{2} , \frac{1}{ 4} , \frac{3}{4} , \frac{4}{4} \)
(b) \(\frac{1}{8} , \frac{2}{ 8} , \frac{3}{8} , \frac{7}{8} \)
(c) \(\frac{2}{5} , \frac{3}{ 5} , \frac{8}{5} , \frac{4}{5} \)

Answer :

Q.2 Express the following as mixed fractions:
(a)\(\frac{20}{3} \)
(b) \(\frac{11}{5} \)
(c) \(\frac{17}{7} \)
(d) \(\frac{28}{5} \)
(e) \(\frac{19}{6} \)
(f) \(\frac{35}{9} \)

Answer :

(a)\(\frac{20}{3} \) = \( 6 \frac{2}{3} \)
(b) \(\frac{11}{5} \) = \( 2 \frac{1}{5} \)
(c) \(\frac{17}{7} \) = \( 2 \frac{3}{7} \)
(d) \(\frac{28}{5} \) = \( 5 \frac{3}{5} \)
(e) \(\frac{19}{6} \) = \( 3 \frac{1}{6} \)
(f) \(\frac{35}{9} \) = \( 3 \frac{8}{9} \)

Q.3 Express the following as improper fractions:
(a) \(7\frac{3}{4} \)
(b) \(5\frac{6}{7} \)
(c) \(2\frac{5}{6} \)
(d) \(10\frac{3}{5} \)
(e) \(9\frac{3}{7} \)
(f) \(8\frac{4}{9} \)

Answer :

(a) \(\frac{(7 × 4 + 3)}{4} = \frac{31}{4} \)

\(\therefore \) The improper form is \(\frac{31}{4} \)
(b) \(\frac{(5 × 7 + 6)}{7} = \frac{41}{7} \)

\(\therefore \) The improper form is \(\frac{41}{7} \)
(c) \(\frac{(2 × 6 + 5)}{6} = \frac{17}{6} \)

\(\therefore \) The improper form is \(\frac{17}{6} \)
(d) \(\frac{(10 × 5 + 3)}{5} = \frac{53}{5} \)

\(\therefore \) The improper form is \(\frac{53}{5} \)
(e) \(\frac{(9 × 7 + 3)}{7} = \frac{66}{7} \)

\(\therefore \) The improper form is \(\frac{66}{7} \)
(f) \(\frac{(8 × 9 + 4)}{9} = \frac{76}{9} \)

\(\therefore \) The improper form is \(\frac{76}{9} \)

Q.1 Write the fractions. Are all these fractions equivalent?

Answer :

(a)
(i) The shaded portion is \(\frac{1}{2} \)
(ii) The shaded portion is\(\frac{2}{4} = \frac{1}{2} \)
(iii) The shaded portion is \(\frac{3}{6} = \frac{1}{2} \)
(iv) The shaded portion is \(\frac{4}{8} = \frac{1}{2} \)
Hence, all fractions are equivalent.
(b)
(i) The shaded portion is \(\frac{4}{12} = \frac{1}{3} \)
(ii) The shaded portion is\(\frac{3}{9} = \frac{1}{3} \)
(iii) The shaded portion is \(\frac{2}{6} = \frac{1}{3} \)
(iv) The shaded portion is \(\frac{6}{15} = \frac{2}{5} \)
Hence, all fractions are not equivalent.

Q.2 Write the fractions and pair up the equivalent fractions from each row.

Answer :

(a)\(\frac{1}{2} \)
(b) \(\frac{4}{6} \) = \(\frac{2}{3} \)
(c) \(\frac{3}{9} \) = \(\frac{1}{3} \)
(d) \(\frac{2}{8} \) = \(\frac{1}{4} \)
(e) \(\frac{3}{4} \)
(i) \(\frac{6}{18} \) = \(\frac{1}{3} \)
(ii) \(\frac{4}{8} \) = \(\frac{1}{2} \)
(iii) \(\frac{12}{16} \) = \(\frac{3}{4} \)
(iv) \(\frac{8}{12} \) = \(\frac{2}{3} \)
(v) \(\frac{4}{16} \) = \(\frac{1}{4} \)
The following are the equivalent fractions
(a) and (ii)
(b) and (iv)
(c) and (i)
(d) and (v)
(e) and (iii)

Q.3 Replace \(\square \)in each of the following by the correct number:
(a) \(\frac{2}{7} = \frac{8}{\square } \)
(b) \(\frac{5}{8} = \frac{10}{\square } \)
(c) \(\frac{3}{5}= \frac{\square }{20} \)
(d) \(\frac{45}{60} = \frac{15}{\square } \)
(e) \(\frac{18}{24}= \frac{\square }{4} \)

Answer :

(a) \(\frac{2}{7} = \frac{8}{\square } \)
\(\rightarrow \) \(\frac{2×4}{7×4} = \frac{8}{28} \)
(b) \(\frac{5}{8} = \frac{10}{\square } \)
\(\rightarrow \) \(\frac{5×2}{8×2} = \frac{10}{16} \)
(c) \(\frac{3}{5}= \frac{\square }{20} \)
\(\rightarrow \) \(\frac{3×4}{5×4} = \frac{12}{20} \)
(d) \(\frac{45}{60} = \frac{15}{\square } \)
\(\rightarrow \) \(\frac{45÷3}{60÷3} = \frac{15}{20} \)
(e) \(\frac{18}{24}= \frac{\square }{4} \)
\(\rightarrow \) \(\frac{18÷6}{24÷6} = \frac{3}{4} \)

Q.4 Find the equivalent fraction of \(\frac{3}{5} \)having
(a) denominator 20
(b) numerator 9
(c) denominator 30
(d) numerator 27

Answer :

(a) We require denominator 20
Let M be the numerator of the fractions
\(\therefore \frac{M}{20} = \(\frac{3}{5} \)
5 × M = 20 × 3
M = (20 × 3) ÷ 5 = 12
Therefore the required fraction is \(\frac{12}{20} \)
(b) We require numerator 9
Let N be the denominator of the fractions
\(\therefore \frac{9}{N} = \(\frac{3}{5} \)
3 × N = 9 × 5
N = (9 × 5) ÷ 3 = 15
Therefore the required fraction is \(\frac{9}{15} \)
(c) We require denominator 30
Let D be the numerator of the fraction
\(\therefore \frac{D}{30} = \(\frac{3}{5} \)
5 × D = 3 × 30
D = (3 × 30) ÷ 5
= 18
Therefore the required fraction is \(\frac{18}{30} \)
(d) We require numerator 27
Let X be the denominator of the fraction
\(\therefore \frac{27}{X} = \(\frac{3}{5} \)
3 × X = 5 × 27
X = (5 × 27) ÷ 3 = 45
Therefore the required fraction is \(\frac{27}{45} \)

Q.5 Find the equivalent fraction of 36 / 48 with
(a) numerator 9
(b) denominator 4

Answer :

(a) Given numerator = 9
\(\therefore \frac{9}{X} = \frac{36}{48} \)

X × 36 = 9 × 48
X = (9 × 48) / 36
X = 12
Hence, the equivalent fraction is \(\frac{9}{12} \)
(b) Given, denominator = 4
\(\therefore \frac{X}{4} = \frac{36}{48} \)

X × 48 = 4 × 36
X = (4 × 36) / 48 = 3
Hence, the equivalent fraction is \(\frac{3}{4} \)

Q.6 Check whether the given fractions are equivalent:
(a) \(\frac{5}{9} , \frac{30}{54} \)
(b) \(\frac{3}{10} , \frac{12}{50} \)
(c) \(\frac{7}{13} , \frac{5}{11} \)

Answer :

(a) Given \(\frac{5}{9} \) and \(\frac{30}{54} \)
We have 5× 54 = 270
9 × 30 = 270
5 × 54 = 9 × 30
Hence, \(\frac{5}{9} \) and \(\frac{30}{54} \) are equivalent fractions
(b) Given \(\frac{3}{10} \) and \(\frac{12}{50} \)
We have 3 × 50 = 150
10 × 12 = 120
3 × 50 \(\neq \)10 × 12
Hence, \(\frac{3}{10} \) and \(\frac{12}{50} \) are not equivalent fractions
(c) Given \(\frac{7}{13} \) and \(\frac{5}{11} \)

We have 7 × 11 = 77
5 × 13 = 65
7 × 11 \(\neq \) 5 × 13
Hence, \(\frac{7}{13} \) and \(\frac{5}{11} \) are not equivalent fractions

Q.7 Reduce the following fractions to simplest form:
(a) \(\frac{48}{60} \)
(b) \(\frac{150}{60} \)
(c) \(\frac{84}{98} \)
(d) \(\frac{12}{52} \)
(e) \(\frac{7}{28} \)

Answer :

(a) \(\frac{48}{60} \) = \(\frac{48÷12}{60÷12} \)
= \(\frac{4}{5} \)
(b) \(\frac{150}{60} \) = \(\frac{150÷30}{60÷30} \)
= \(\frac{5}{2} \)
(c) \(\frac{84}{98} \)= \(\frac{84÷14}{98÷14} \)
= \(\frac{6}{7} \)
(d) \(\frac{12}{52} \) = \(\frac{12÷4}{52÷4} \)
= \(\frac{3}{13} \)
(e) \(\frac{7}{28} \) = \(\frac{7÷7 }{28÷7 } \)
= \(\frac{1}{4} \)

Q.8 Ramesh had 20 pencils, Sheelu had 50 pencils and Jamaal had 80 pencils. After 4 months, Ramesh used up 10 pencils, Sheelu used up 25 pencils and Jamaal used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of her/his pencils?

Answer :

Total number of pencils Ramesh had = 20
Number of pencils used by Ramesh = 10
\(\therefore \) Fraction = \(\frac{10}{20} = \frac{1}{2} \)
Total number of pencils Sheelu had = 50
Number of pencils used by Sheelu = 25
\(\therefore \) Fraction = \(\frac{25}{50} = \frac{1}{2} \)
Total number of pencils Jamaal had = 80
Number of pencils used by Jamaal = 40
\(\therefore \) Fraction = \(\frac{40}{80} = \frac{1}{2} \)
Yes, each has used up an equal fraction of pencils i.e \(\frac{1}{2} \)

Q.9 Match the equivalent fractions and write two more for each.
(i) \(\frac{250}{400} \) (a) \(\frac{2}{3} \)
(ii) \(\frac{180}{200} \) (b) \(\frac{2}{5} \)
(iii) \(\frac{660}{990} \) (c) \(\frac{1}{2} \)
(iv) \(\frac{180}{360} \) (d) \(\frac{5}{8} \)
(v) \(\frac{220}{550} \) (e) \(\frac{9}{10} \)

Answer :

(i) \(\frac{250}{400} \) = (d) \(\frac{5}{8} \)
(ii) \(\frac{180}{200} \) = (e) \(\frac{9}{10} \)
(iii) \(\frac{660}{990} \) = (a) \(\frac{2}{3} \)
(iv) \(\frac{180}{360} \) = (c) \(\frac{1}{2} \)
(v) \(\frac{220}{550} \) = (b) \(\frac{2}{5} \)

Q.1 Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign ‘’ between the fractions:

(c) Show\(\frac{2}{6} , \frac{4}{6} , \frac{8}{6} and \frac{6}{6} \) on the number line. Put appropriate signs between the fractions given.
\(\frac{5}{6} \square \frac{2}{6} , \frac{3}{6} \square 0, \frac{1}{6} \square \frac{6}{6} , \frac{8}{6} \square \frac{5}{6}

Answer :

(a) \(\frac{3}{8} , \frac{6}{8} , \frac{4}{8} and \frac{1}{8} \)
Ascending order = \(\frac{1}{8} < \frac{3}{8} < \frac{4}{8} < \frac{6}{8} \)
Decending order = \(\frac{6}{8} > \frac{4}{8} > \frac{3}{8} > \frac{1}{8} \)
(b) \(\frac{8}{9} , \frac{4}{9} , \frac{3}{9} and \frac{6}{9} \)
Ascending order = \(\frac{3}{9} < \frac{4}{9} < \frac{6}{9} < \frac{8}{9} \)
Decending order = \(\frac{8}{9} > \frac{6}{9} > \frac{4}{9} > \frac{3}{9} \)
(c)
\(\frac{5}{6} > \frac{2}{6} , \frac{3}{6} > 0, \frac{1}{6} < \frac{6}{6} , \frac{8}{6} > \frac{5}{6}

Q.2 Compare the fractions and put an appropriate sign.
(a)\( \frac{3}{6} \square \frac{5}{6} \)
(b) \( \frac{1}{7} \square \frac{1}{4} \)
(c) \( \frac{4}{5} \square \frac{5}{5} \)
(d)\( \frac{3}{5} \square \frac{3}{7} \)

Answer :

(a)\( \frac{3}{6} < \frac{5}{6} \)
If denominators are same than whose numerator is greater that fraction also greater.
(b) \( \frac{1}{7} \ < \frac{1}{4} \)
If denominators are same than whose numerator is greater that fraction also greater.
(c) \( \frac{4}{5} < \frac{5}{5} \)
If denominators are same than whose numerator is greater that fraction also greater.

(d)\( \frac{3}{5} > \frac{3}{7} \)
If denominators are same than whose numerator is greater that fraction also greater.

Q.3 Make five more such pairs and put appropriate signs.

Answer :

(a) \(\frac{6}{9} < \frac{8}{9} \)
(b) \(\frac{13}{7} > \frac{6}{7} \)
(c) \(\frac{15}{9} < \frac{15}{7} \)
(d) \(\frac{7}{8} > \frac{5}{8} \)
(e) \(\frac{2}{9} < \frac{6}{9} \)

Q.4 Look at the figures and write ’<’, or ’>’ ’=’ between the given pairs of fractions.

(a) \(\frac{1}{6} \square \frac{1}{3} \)
(b) \(\frac{3}{4} \square \frac{2}{6} \)
(c) \(\frac{2}{3} \square \frac{2}{4} \)
(d) \(\frac{6}{6} \square \frac{3}{3} \)
(e) \(\frac{5}{6} \square \frac{5}{5} \)

Answer :

(a) \(\frac{1}{6} < \frac{1}{3} \)
(b) \(\frac{3}{4} > \frac{2}{6} \)
(c) \(\frac{2}{3} > \frac{2}{4} \)
(d) \(\frac{6}{6} = \frac{3}{3} \)
(e) \(\frac{5}{6} < \frac{5}{5} \)

Q.5 How quickly can you do this? Fill appropriate sign. ( ‘<’, ‘=’, ‘>’)
(a) \(\frac{1}{2} \square \frac{1}{5} \)
(b) \(\frac{2}{4} \square \frac{3}{6} \)
(c) \(\frac{3}{5} \square \frac{2}{3} \)
(d) \(\frac{3}{4} \square \frac{2}{8} \)
(e) \(\frac{3}{5} \square \frac{5}{5} \)
(f) \(\frac{7}{9} \square \frac{3}{9} \)
(g) \(\frac{1}{4} \square \frac{2}{8} \)
(h) \(\frac{6}{10} \square \frac{4}{5} \)
(i) \(\frac{3}{4} \square \frac{7}{8} \)
(j) \(\frac{6}{10} \square \frac{3}{5} \)
(k) \(\frac{5}{7} \square \frac{15}{21} \)

Answer :

(a) \(\frac{1}{2} \square \frac{1}{5} \)
\(\frac{1}{2} and \frac{1}{5} \)
5 × 1 \(\square \) 2 × 1
5 > 2
Hence, \(\frac{1}{2} > \frac{1}{5} \)
(b) \(\frac{2}{4} \square \frac{3}{6} \)
\(\frac{2}{4} and \frac{3}{6} \)
6 × 2 \(\square \) 4 × 3
12 = 12
Hence, \(\frac{2}{4} = \frac{3}{6} \)
(c) \(\frac{3}{5} \square \frac{2}{3} \)
\(\frac{3}{5} and \frac{2}{3} \)
3 × 3 \(\square \) 5 × 2
9 < 10
Hence,\(\frac{3}{5} < \frac{2}{3} \)
(d) \(\frac{3}{4} \square \frac{2}{8} \)
\(\frac{3}{4} and \frac{2}{8} \)
3 × 8 \(\square \) 4 × 2
24 < 8
Hence,\(\frac{3}{4} > \frac{2}{8} \)
(e) \(\frac{3}{5} \square \frac{5}{5} \)
\(\frac{3}{5} and \frac{5}{5} \)
3 × 5 \(\square \) 5 × 5
15 < 25
Hence,\(\frac{3}{5} < \frac{5}{5} \)
(f) \(\frac{7}{9} \square \frac{3}{9} \)
\(\frac{7}{9} and \frac{3}{9} \)
9 × 7 \(\square \) 9 × 3
63 > 27
Hence,\(\frac{7}{9} > \frac{3}{9} \)
(g) \(\frac{1}{4} \square \frac{2}{8} \)
\(\frac{1}{4} and \frac{2}{8} \)
1 × 8 \(\square \) 4 × 2
8 = 8
Hence,\(\frac{1}{4} = \frac{2}{8} \)
(h) \(\frac{6}{10} \square \frac{4}{5} \)
\(\frac{6}{10} and \frac{4}{5} \)
5 × 6 \(\square \) 10 × 4
30 < 40
Hence,\(\frac{6}{10} < \frac{4}{5} \)
(i) \(\frac{3}{4} \square \frac{7}{8} \)
\(\frac{3}{4} and \frac{7}{8} \)
3 × 8 \(\square \) 4 × 7
24 < 28
Hence,\(\frac{3}{4} < \frac{7}{8} \)
(j) \(\frac{6}{10} \square \frac{3}{5} \)
\(\frac{6}{10} and \frac{3}{5} \)
5 × 6 \(\square \) 10 × 3
30 = 30
Hence,\(\frac{6}{10} = \frac{3}{5} \)
(k) \(\frac{5}{7} \square \frac{15}{21} \)
\(\frac{5}{7} and \frac{15}{21} \)
5 × 21 \(\square \) 7 × 15
105 = 105
Hence,\(\frac{5}{7} = \frac{15}{21} \)

Q.6 The following fractions represent just three different numbers. Separate them into three groups of equivalent fractions, by changing each one to its simplest form.
(a) \(\frac{2}{12} \)
(b) \(\frac{3}{15} \)
(c) \(\frac{8}{50} \)
(d) \(\frac{16}{100} \)
(e) \(\frac{10}{60} \)
(f) \(\frac{15}{75} \)
(g) \(\frac{12}{60} \)
(h) \(\frac{16}{96} \)
(i) \(\frac{12}{75} \)
(j) \(\frac{12}{72} \)
(k) \(\frac{3}{18} \)
(l) \(\frac{4}{25} \)

Answer :

(a) \(\frac{2}{12} = \frac{2÷2}{12÷2} = \frac{1}{6} \)
(b) \(\frac{3}{15} = \frac{3÷3}{15÷3} = \frac{1}{5} \)
(c) \(\frac{8}{50} = \frac{8÷2}{50÷2} = \frac{4}{25} \)
(d) \(\frac{16}{100} = \frac{16÷4}{100÷4} = \frac{4}{25} \)
(e) \(\frac{10}{60} = \frac{10÷10}{60÷10} = \frac{1}{6} \)
(f) \(\frac{15}{75} = \frac{15÷15}{75÷15} = \frac{1}{5} \)
(g) \(\frac{12}{60} = \frac{12÷12}{60÷12} = \frac{1}{5} \)
(h) \(\frac{16}{96} = \frac{16÷16}{196÷16} = \frac{1}{6} \)
(i) \(\frac{12}{75} = \frac{12÷3}{75÷3} = \frac{4}{25} \)
(j) \(\frac{12}{72} = \frac{12÷12}{72÷12} = \frac{1}{6} \)
(k)\(\frac{3}{18} = \frac{3÷3}{18÷3} = \frac{1}{6} \)
(l) \(\frac{4}{25} \)
Totally there are 3 groups of equivalent fractions.
\(\frac{1}{6} \)= (a), (e), (h), (j), (k)
\(\frac{1}{5} \) = (b), (f), (g)
\(\frac{4}{25} \) = (c), (d), (i), (l)

Q.7 Find answers to the following. Write and indicate how you solved them.
(a) Is \(\frac{5}{9} \) equal to \(\frac{4}{5} \)
(b) Is \(\frac{9}{16} \) equal to \(\frac{5}{9} \)
(c) Is \(\frac{4}{5} \) equal to \(\frac{16}{20} \)
(d) Is \(\frac{1}{15} \) equal to \(\frac{4}{30} \)

Answer :

(a) Is \(\frac{5}{9} \) equal to \(\frac{4}{5} \)
by cross multiplication
5 × 5 \(\square \) 9 × 4
25 \(\neq \) 36
\(\frac{5}{9} \) \(\neq \) \(\frac{4}{5} \)
(b) Is \(\frac{9}{16} \) equal to \(\frac{5}{9} \)
by cross multiplication
9 × 9 \(\square \) 16 × 5
81 \(\neq \) 80
\(\frac{9}{16} \) \(\neq \) \(\frac{5}{9} \)
(c) Is \(\frac{4}{5} \) equal to \(\frac{16}{20} \)
by cross multiplication
20 × 4 \(\square \) 16 × 5
80 = 80
\(\frac{4}{5} \) \(\neq \) \(\frac{16}{20} \)
(d) Is \(\frac{1}{15} \) equal to \(\frac{4}{30} \)
by cross multiplication
30 × 1 \(\square \) 4 × 15
30 \(\neq \) 60
\(\frac{1}{15} \) \(\neq \) \(\frac{4}{30} \)

Q.8 Ila read 25 pages of a book containing 100 pages. Lalita read \(\frac{2}{5} \) of the same book. Who read less?

Answer :

Ila read 25 pages out of 100 pages
Fraction = \(\frac{25}{100} = \frac{25÷25}{100÷25} = \frac{1}{4} \)
Lalita read =\( \frac{2}{5} \)
\( \frac{2}{5} and \frac{1}{4} \)
By cross multiplication
4 × 2 and 5 ×1 8 > 5
\( \frac{2}{5} > \frac{1}{4} \)
Hence Lalita read less.

Q.9 Rafiq exercised for \(\frac{3}{6} \)of an hour, while Rohit exercised for \(\frac{3}{4} \) of an hour. Who exercised for a longer time?

Answer :

Rafiq exercised for\(\frac{3}{6} \) of an hour.
Rohit exercised for \(\frac{3}{4} \) of an hour.
\(\frac{3}{6} \) and \(\frac{3}{4} \)
by cross multiplication
3 x 4 = 12 and 3 x 6 = 18
Since 12 < 18
\(\therefore \frac{3}{4} > \frac{3}{6} \)
Hence Rohit exercised for longer time.

Q.10 In a class A of 25 students, 20 passed with 60% or more marks; in another class B of 30 students, 24 passed with 60% or more marks. In which class was a greater fraction of students getting with 60% or more marks?

Answer :

In class A, 20 students passed in first class out of 25 students.
\(\therefore \) Fraction of students getting first class
\(\frac{20}{25} = \frac{20÷5}{25÷5} = \frac{4}{5} \)
In class B, 24 students passed in first class out of 30 students.
\(\therefore \)Fraction of students getting first class
\(\frac{24}{30} = \frac{24÷6}{30÷6} = \frac{4}{5} \)
Comparing the two fractions, we get\(\frac{4}{5} = \frac{4}{5} \)
Hence, both the class A and B have the same fractions.

Q.1 Write these fractions appropriately as additions or subtractions:

Answer :

(a) The given figure represents the addition of
\(\frac{1}{5} + \frac{2}{5} = \frac{3}{5} \)
(b) The given figure represents the addition of
\(\frac{5}{5} + \frac{3}{5} = \frac{2}{5} \)
(c) The given figure represents the addition of
\(\frac{2}{6} + \frac{3}{6} = \frac{5}{6} \)

Q.2 Solve:
(a) \(\frac{1}{18} + \frac{1}{18} \)
(b) \(\frac{8}{15} + \frac{3}{15} \)
(c) \(\frac{7}{7} - \frac{5}{7} \)
(d) \(\frac{1}{22} + \frac{21}{22} \)
(e) \(\frac{12}{15} - \frac{7}{15} \)
(f) \(\frac{5}{8} + \frac{3}{8} \)
(g) 1 – \(\frac{2}{3} \) (1 = \(\frac{3}{3} \) )
(h) \(\frac{1}{4} + \frac{0}{4} \)
(i) 3 - \frac{12}{5} \)

Answer :

(a) \(\frac{1}{18} + \frac{1}{18} \) = \(\frac{2}{18} = \frac{1}{9} \)
(b) \(\frac{8}{15} + \frac{3}{15} \) = \(\frac{11}{15} \)
(c) \(\frac{7}{7} - \frac{5}{7} \) = \(\frac{2}{7} \)
(d) \(\frac{1}{22} + \frac{21}{22} \) = \(\frac{22}{22} \) = 1
(e) \(\frac{12}{15} - \frac{7}{15} \) = \(\frac{5}{15} \) = \(\frac{1}{5} \)
(f) \(\frac{5}{8} + \frac{3}{8} \) = \(\frac{8}{8} \) = 1
(g) 1 – \(\frac{2}{3} \) (1 = \(\frac{3}{3} \) )
= \(\frac{3}{3} \) - \(\frac{2}{3} \) = \(\frac{1}{3} \)
(h) \(\frac{1}{4} + \frac{0}{4} \) = \(\frac{1}{4} \)
(i) 3 - \frac{12}{5} \) = \(\frac{15-12}{5} \) = \(\frac{3}{5} \)

Q.3 Shubham painted \(\frac{2}{3} \) of the wall space in his room. His sister Madhavi helped and painted \(\frac{1}{3} \) of the wall space. How much did they paint together?

Answer :

Fraction of wall painted by Shubham = \(\frac{2}{3} \)
Fraction of wall painted by Madhavi = \(\frac{1}{3} \)
Fraction of wall painted by Shubham and Madhavi
= \(\frac{2}{3} + \frac{1}{3} = \frac{3}{3} = 1 \)
\(\therefore \) Shubham and Madhavi together painted 1 complete wall in a room.

Q.4. Fill in the missing fractions. (a) \(\frac{7}{10} - \square = \frac{3}{10} \)
(b)\(\square - \frac{3}{21} = \frac{5}{21} \)
(c) \(\square - \frac{3}{6} = \frac{3}{6} \)
(d) \(\square + \frac{5}{27} = \frac{12}{27} \)

Answer :

(a) \(\frac{7}{10} \square = \frac{3}{10} \)
Or, \( - \square = \frac{3}{10} - \frac{7}{10} \)
Or, \(-\square = - \frac{4}{10} = -\frac{2}{5} \)
Or, \(\square = \frac{2}{5} \)
(b) \(\square - \frac{3}{21} = \frac{5}{21} \)
Or, \(\square = \frac{5}{21} + \frac{3}{21} \)
Or, \(\square = \frac{8}{21} \)
(c) \(\square - \frac{3}{6} = \frac{3}{6} \)
Or, \(\square = \frac{3}{6} + \frac{3}{6} \)
Or, \(\square = \frac{6}{6} = 1 \) (d) \(\square + \frac{5}{27} = \frac{12}{27} \)
\(\square = \frac{12}{27} - \frac{5}{27} \)
\(\square = \frac{7}{27} \)

Q.5 Javed was given \(\frac{5}{7} \)of a basket of oranges. What fraction of oranges was left in the basket?

Answer :

Left orange in basket = 1 - \(\frac{5}{7} = \frac{7}{7} - \frac{5}{7} \)
\(\frac{2}{7} \)